Math Problem Statement

(x+2)(x-7)

Solution

To expand the expression (x+2)(x7)(x+2)(x-7), apply the distributive property (also known as the FOIL method for binomials). This involves multiplying each term in the first binomial by each term in the second binomial:

(x+2)(x7)=x(x7)+2(x7)(x+2)(x-7) = x(x-7) + 2(x-7)

Now, distribute:

=x27x+2x14= x^2 - 7x + 2x - 14

Finally, combine the like terms:

x25x14x^2 - 5x - 14

So, the expanded form of (x+2)(x7)(x+2)(x-7) is:

x25x14x^2 - 5x - 14

Would you like further details or have any questions? Here are 5 related questions:

  1. What is the factored form of x25x14x^2 - 5x - 14?
  2. Can you find the roots of the equation (x+2)(x7)=0(x+2)(x-7) = 0?
  3. How would you complete the square for the expression x25x14x^2 - 5x - 14?
  4. How do you graph y=(x+2)(x7)y = (x+2)(x-7) or y=x25x14y = x^2 - 5x - 14?
  5. How does the discriminant help in solving quadratic equations like x25x14=0x^2 - 5x - 14 = 0?

Tip: Always simplify expressions by combining like terms where possible to get the cleanest form.

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Math Problem Analysis

Mathematical Concepts

Algebra
Binomial Expansion
Factoring
Quadratic Equations

Formulas

Distributive property: (a + b)(c + d) = ac + ad + bc + bd
Quadratic equation standard form: ax^2 + bx + c = 0

Theorems

Distributive Property

Suitable Grade Level

Grades 8-10